- #1
Irks23
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Homework Statement
If the product of two matrices is zero, it is not necessary that either one be zero. In particular, show that a 2 x 2 matrix who's square is zero may be written in two parameters a and b, and find the general form of the matrix. Verify that it's determinant is 0.
The Attempt at a Solution
So I tried to find a 2 x 2 matrix who's square is 0 and determinant is 0. The best I could come up with was:
A iA
iA A
which squares to:
0 2iA^2
2iA^2 0
but only the real part is 0, not the imaginary part, and the determinant is not zero. I'm not seeing at this point how any matrix's square could be zero except the 0 matrix, am I interpreting the question wrong?